Related papers: A Truly Conformable Calculus on Time Scales
We derive the Helmholtz theorem for Hamiltonian systems defined on time scales in the context of nonshifted calculus of variations which encompass the discrete and continuous case. Precisely, we give a theorem characterizing first order…
Conformal prediction is a powerful post-hoc framework for uncertainty quantification that provides distribution-free coverage guarantees. However, these guarantees crucially rely on the assumption of exchangeability. This assumption is…
In probabilistic coherence spaces, a denotational model of probabilistic functional languages, morphisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives…
We study the complexity of deterministic and probabilistic inversions of partial computable functions on the reals.
A multifractal-like representation for multi-time multi-scale velocity correlation in turbulence and dynamical turbulent models is proposed. The importance of subleading contributions to time correlations is highlighted. The fulfillment of…
We define a generalization of convex functions, which we call $\delta$-convex functions, and show they must satisfy interior H\"older and $W^{1,p}$ estimates. As an application, we consider solutions of a certain class of fully nonlinear…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
A simple proof is given of the known fact that an m-times continuously differentiable function on the real line can be approximated along with its derivatives by an entire function and its respective derivatives.
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
This document introduces a generalization of calculus that treats both continuous and discrete variables on an equal footing. This generalization of calculus was developed independently of the "Calculus on Time Scales" literature but may be…
We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove…
The Caputo time-derivative is usually defined pointwise for well-behaved functions, say, for continuously differentiable functions. Accordingly, in the theory of the partial fractional differential equations with the Caputo derivatives, the…
This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative.
We study various proofs of the caracterization of constant functions, more precisely of the theorem: a derivable function, defined on a real interval, is constant if, and only if, its derivative is null. Our aim is to study the…
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…
Cycle integrals of modular functions are expected to play a role in real quadratic analogue of singular moduli. In this paper, we extend the definition of cycle integrals of modular functions from real quadratic numbers to badly…
Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…
In this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated. These theories are realized in terms of free scalar fields starting from the simple $b-c$ systems and scalar fields on…
Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting…
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…